Yes, it is definitely still safe to eat. That liquid is known as WHEY and it contains some protein, enzymes and beneficial bacteria. You can stir it back into the yogurt to keep the texture more creamy or you can drain it off and add it to smoothies. Here are some other ideas on how you can repurpose whey: http://www.bonappetit.com/test-kitchen/ingredients/article/what-is-yogurt-whey
When Greek yogurt is made, whey is strained off so you are left with a more concentrated product that is thicker. It also takes more milk to make Greek yogurt than it does to make a regular plain yogurt. There is nothing particularly "Greek" about Greek yogurt, it just refers to the style, i.e. a strained yogurt that is thicker and creamier with higher protein and lower carbohydrates than regular yogurt.
Leah McGrath, RDN, LDN
Ingles Markets Corporate Dietitian